L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term

The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose method for solving diffusion equation with nonlocal term. proposed comprises L1 scheme on graded mesh, finite element and Newton’s method. We discuss well-posedness formulation at discrete level derive priori error estimates fully-discrete L2(Ω) H1(Ω) norms. Finally, some numerical experiments are conducted to validate theoretical findings.